Article Babuska

7/31/2019 Article Babuska

1/15

Estimation of respiratory parametersvia fuzzy clustering

R. Babuskaa,*, L. Alica, M.S. Lourensb,A.F.M. Verbraakb, J. Bogaardb

aDepartment of Information Technology and Systems, Control Engineering Laboratory,

Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The NetherlandsbDepartment of Pulmonary and Intensive Care Medicine, Erasmus Medical Centre, Rotterdam,

3015 GD Rotterdam, The Netherlands

Received 24 February 2000; received in revised form 12 July 2000; accepted 1 August 2000

Abstract

The results of monitoring respiratory parameters estimated from owpressurevolume

measurements can be used to assess patients' pulmonary condition, to detect poor patient

ventilator interaction and consequently to optimize the ventilator settings. A new method is

proposed to obtain detailed information about respiratory parameters without interfering with the

expiration. By means of fuzzy clustering, the available data set is partitioned into fuzzy subsets thatcan be well approximated by linear regression models locally. Parameters of these models are then

estimated by least-squares techniques. By analyzing the dependence of these local parameters on

the location of the model in the owvolumepressure space, information on patients' pulmonary

condition can be gained. The effectiveness of the proposed approaches is demonstrated by

analyzing the dependence of the expiratory time constant on the volume in patients with chronic

obstructive pulmonary disease (COPD) and patients without COPD.# 2001 Elsevier Science B.V.

All rights reserved.

Keywords: Respiratory mechanics; Mechanical ventilation; Parameter estimation; Respiratory resistance and

compliance; Expiratory time constant; Fuzzy clustering; Least-squares estimation

1. Introduction

The importance of monitoring respiratory mechanics in patients on ventilatory support is

generally accepted. Respiratory parameters can be used to assess patients' pulmonary

condition, to detect poor patientventilator interaction and consequently to optimize

Artificial Intelligence in Medicine 21 (2001) 91105

* Corresponding author. Tel.: 31-15-2785117; fax: 31-15-2786679.E-mail addresses: [email protected] (R. Babuska), [email protected] (A.F.M. Verbraak).

0933-3657/01/$ see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 9 3 3 - 3 6 5 7 ( 0 0 ) 0 0 0 7 5 - 0


2/15

ventilator settings. Monitoring respiratory mechanics is of paramount importance in

mechanically ventilated patients with chronic obstructive pulmonary disease (COPD).

In these patients, due to the disturbance in respiratory mechanics, it is difcult to set theventilator and weaning from the ventilator is cumbersome. By identifying these patients,

assessing their pulmonary condition and patientventilator interaction, ventilator settings

and medical treatment can be adjusted resulting in a more favorable outcome. The

expiratory time constant provides information on the mechanical properties of the

respiratory system, it is a measure of lung emptying and can be used to predict the

minimal time needed for complete expiration. Several methods have been proposed to

determine the expiratory time constant [13]. However, these methods either interfere with

the expiration [2,3], or assume a linear relationship between ow and volume [1]. The latter

has to be questioned in patients with COPD, in view of the presence of ventilatory

inhomogeneity and expiratory ow limitation. In this article, a new method is proposed to

estimate respiratory parameters without interfering with the expiration. Moreover, themethod is very general in the sense that it does not assume any particular functional

relationship between the ow and volume.

The monitoring of lungs can be accomplished by analyzing the pressure, ow and

volume measurements. Typically, a low-order physical model of the respiratory dynamics

is assumed and parameters in this model are estimated from the data [1,46]. Two main

approaches can be distinguished in the literature: time-domain estimation and frequency-

domain estimation. In this article, the time-domain approach is followed, as it enables us to

gain insight into nonlinear phenomena and exploit for diagnosis the information obtained.

Frequency domain techniques, however, are limited to linear models and are less suitable

for this purpose.

The method presented in this paper uses a straightforward extension of the classical

linear single-compartment model [4,5]. This model describes the dynamic relationbetween the pressure P (hPa), the air ow-rate V (l/min) and the volume V (l) of the lungs

P EV R V P0X (1)

The respiratory elastance E(hPa/l), the resistance R (hPa s/l) and the elastic recoil pressure

P0 (pressure when the volume V equals zero) are free parameters to be estimated from data.

It is well known that this linear model may yield too coarse an approximation of the

given data, especially for patients with pulmonary disorders (such as the COPD). There-

fore, modications of (1) have been proposed [4]. One can, for instance, use different

parameters for inspiration and expiration or nonlinearities can be introduced by consider-

ing E and R to be functions of the volume or the ow [5].

The approach proposed in this paper is based on automatic detection (localization) ofmultiple local linear models. Hence, one does not need to make any assumptions about the

mathematical form or parameterization of the nonlinearity. By observing the dependence

of the local respiratory parameters on the location of the model in the owvolume

pressure space, information about the ventilated subject can be obtained.

The two main techniques used to obtain the parameters of the multiple models are fuzzy

clustering and linear least-squares estimation. By means of fuzzy clustering, the available

data set is partitioned into fuzzy subsets that can be well approximated by linear regression

models locally. Parameters of these models are then estimated by least-squares techniques.

92 R. Babuska et al. / Artificial Intelligence in Medicine 21 (2001) 91105


3/15

The use of clustering techniques is motivated by the fact that they can reveal structures in

data without relying on assumptions common to conventional statistical methods, such as

the underlying statistical distribution. Clustering has been successfully used in a variety ofelds, including classication, image processing, pattern recognition, modeling and

identication. An increasing number of applications can be found in the medical eld.

Typical application domains include image processing for computer-aided diagnosis [79],

signal processing in evoked potentials estimation [10], analysis of time series for imaging

[11], and classication [12].

The current paper is organized as follows. The patients and the respiratory measure-

ments are described in Section 2. The applied methods and algorithms can be found in

Section 3, while Section 4 presents the results obtained for the estimation of the expiratory

time constant. Section 5 gives a discussion of the results, conclusions and suggestions for

future research.

2. Problem description

In this section, the conducted study is described in terms of the patients, the

mechanical ventilation conditions, and the collection and preprocessing of the respiratory

data.

2.1. Patients

Twenty patients admitted to the medical intensive care unit of the Erasmus Medical

Centre in Rotterdam were studied. Patients were included if they fullled the following

criteria: mechanical ventilation via an endotracheal or tracheostomy tube and the absenceof air leaks.

Ten of these patients had a history of severe chronic obstructive pulmonary

disease (COPD) according to the European Respiratory Society consensus; a clinical

diagnosis of COPD and previous lung function data showing a forced expiratory

volume in 1 s (FEV1) less than 50% of predicted normal value (mean 29% of predicted,

range 2137%) [13]. These 10 patients were ventilated because of respiratory failure due to

an exacerbation of their COPD. In the other 10 patients, underlying diseases included a

variety of medical conditions all complicated by respiratory failure and ventilator

dependency.

All patients were mechanically ventilated with the Siemens Servo 300 ventilator

(Siemens-Elema, Solna, Sweden). Ventilator settings were set by the primary physicianand remained unchanged during the study, with the exception that if positive end-

expiratory pressure (PEEP) was present, it was removed. All patients were ventilated

in the volume-controlled mode with an average minute volume of 8.5 l/min (range

6.515.0 l/min). The average respiratory rate was 12 breaths per minute (range 820).

The ratio between inspiratory and expiratory time was 35:65. During the study, the patients

were sedated with midazolam (Roche Nederland B.V., Mijndrecht, The Netherlands).

Informed consent was obtained from the patients or their next of kin. The measurements for

this study were approved of by the local ethics committee.

R. Babuska et al. / Artificial Intelligence in Medicine 21 (2001) 91105 93


4/15

2.2. Respiratory measurements

The ow V was measured by a heated pneumotachometer (Lilly, Jaeger, Wurzburg,

Germany) connected to the endotracheal tube. The airway opening pressureP was measured

proximal to the pneumotachometer by a pressure transducer (Validyne, Validyne Co.,

Northridge, USA). A 12-bit AD converter was used to convert the measured analog signals

to digital data at a sampling frequency of 100 Hz. Data were stored and analyzed using a

personal computer. On average, 3000 samples were used for the analysis of each patient.

The rst two panels of Fig. 1 show typical pressure and ow-rate signals for a

representative patient without COPD. The bottom panel gives the volume V obtained

by numerical integration of the sampled ow signal. Note that a drift in the volume signal

occurs, which is mainly caused by leakage and by the difference in temperature and relativehumidity between inspiration and expiration. This drift can be partially removed by adding

an offset signal obtained by tting a line or a low-order polynomial trough the volume

minima in the individual cycles.

3. Parameter estimation through fuzzy clustering

This section presents the methods and algorithms applied to the analysis of the data and

parameter estimation.

Fig. 1. Sample data set of a representative patient without COPD.



5/15

3.1. The data set to be clustered

In our application, the data are the sampled measurements of the pressure, ow andvolume. Generally, there can be any observations, each consisting ofn measured variables,

grouped into an n-dimensional column vector zk z1kY F F F YznkT

, zk P Rn. A set of N

observations is denoted by Z fzkjk 1Y 2Y F F F YNg, and is represented as an n Nmatrix:

Z

z11 z12 z1Nz21 z22 z2NFFF FF

F FFF FF

F

zn1 zn2 znN

PTTTR

QUUUSX (2)

In the analysis of respiratory measurement, each column ofZ is generally the ow

volumepressure triplet:zk VkY VkYPkT, although only some of these signals can

be used when clustering is applied locally to the inspiration or expiration phase. Details can

be found in Section 4.

3.2. Fuzzy partition

The objective of clustering is to partition the data set Z into c clusters. Fuzzy partition of

Z is a family of fuzzy subsets fAij1 i cg. The subsets are dened by their membership(characteristic) functions, represented in the partition matrix U mikcN. The ith row ofthis matrix contains values of the membership function of the ith fuzzy subset Ai ofZ. The

partition matrix satises the following conditions:

mik P 0Y 1Y 1 i cY 1 k NY (3a)

ci1

mik 1Y 1 k NY (3b)

0 `Nk1

mik ` NY 1 i cX (3c)

Eq. (3a) states the well-known fact that the membership degrees are real numbers from the

interval 0Y 1. Condition (3b) constrains the sum of each column to 1, and thus the totalmembership of eachzk in all the clusters equals one. Eq. (3c) means that none of the fuzzy

subsets is empty nor it contains all the data.Let us illustrate the concept of fuzzy partition by a simple example. Consider a data set

Z z1Yz2Y F F F Yz9, shown in Fig. 2.By using multiple-model regression, this data set can be approximated by two lines (data

points z1 toz4 andz6 toz9, respectively). Note that pointz5 does not fully belong to either of

the models. The corresponding fuzzy partition ofZ is:

U1X0 1X0 1X0 1X0 0X5 0X0 0X0 0X0 0X00X0 0X0 0X0 0X0 0X5 1X0 1X0 1X0 1X0

!X



6/15

The rst row ofU denes the membership function for the rst subset A1, the second

row denes the membership function of the second subset A2. Membership degrees ofz5 reect the fuzziness of the partition. Note that the sum of the rows is one for all data

points.

3.3. Clustering algorithm

In this application, the fuzzy partition matrix is obtained by applying the Gustafson

Kessel (GK) algorithm [14], based on the minimization of the well-known fuzzy c-means

functional:

JZYUYVY fAig ci1

Nk1

mikm

D2ikAi Y (4)

where U mik is the fuzzy partition matrix ofZ, V v1Y v2Y F F F Y vc, vi P Rn is a vector

of cluster prototypes (centers), which have to be determined, and

D2ikAi zk viTAizk vi (5)

is the squared inner-product distance norm. Matrices Ai are computed in the optimization

algorithm using the local covariance of the data around each cluster center. This allows

each cluster to adapt the distance norm to the local distribution of the data. If the data

samples are distributed along a nonlinear hypersurface, the GK algorithm will nd clusters

that are local linear approximations of this hypersurface. The overlap of the clusters is

controlled by the user-dened parameter m P 1YI.

The minimization of (4) represents a nonlinear optimization problem that is usuallysolved by using the Picard iteration through the rst-order conditions for stationary points

of (4). This algorithm is stated (without derivation) in Algorithm 1.

Algorithm 1. GustafsonKessel (GK) algorithm

Given the data set Z, choose the number of clusters 1 ` c ` N, the weighting exponentm b 1 and the termination tolerance E b 0. Initialize the partition matrix randomly, suchthat it satises conditions (3a)(3c).

Fig. 2. A sample data set in R2.



7/15

Repeat for l 1Y 2Y F F F

Step 1: Compute cluster prototypes (means):

vli

Nk1m

l1ik

mzkN

k1ml1ik

mY 1 i cX

Step 2: Compute the cluster covariance matrices:

Fi

Nk1m

l1ik

mzk vli zk v

li

T

Nk1m

l1ik

mY 1 i cX

Step 3: Compute the distances:

D2ikAi zk vli

TdetFi1anF

1i zk v

li Y 1 i cY 1 k NX

Step 4: Update the partition matrix:

for 1 k Nif DikAi b 0 for 1 i c,

mlik

1cj1DikAiaDjkAj

2am1Y

otherwise

mlik 0 ifDikAi b 0Y and m

lik P 0Y 1with

ci1

mlik 1Y

until k Ul Ul1 k` E.

Appendix A contains a MATLAB implementation of the algorithm.

The following parameters must be specied before clustering: the number of clusters, c,

the `fuzziness' exponent, m, the termination tolerance, E. The choices for these parameters

are now discussed.

3.3.1. Number of clusters

The number of clusters can either be selected a priori or it can be automaticallydetermined by using cluster validity measures [1517] or by iterative merging or insertion

of clusters [18,19]. In this paper, c is a user-dened parameter.

3.3.2. Fuzziness parameter

The weighting exponent m inuences the fuzziness of the resulting partition. As m

approaches one from above, the partition becomes hard (non-fuzzy) (mik P f0Y 1g)andas mgoes to I, the partition becomes completely fuzzy (mik 1ac). The standard value m 2is used in this paper.



8/15

3.3.3. Termination criterion

The GK algorithm stops iterating when the norm of the difference between U in two

successive iterations is smaller than the termination parameter E. For the maximum normmaxikjm

lik m

l1ik j, the usual choice is E 0X01.

3.4. Least-square estimation of the respiratory parameters

The GK algorithm yields a partition matrix which determines to what degree the

individual data samples belong to the individual linear submodels. In order to estimate the

parameters of these submodels, the fuzzy partition is rst converted into a crisp one by

applying an a-cut. This means that only the data samples that belong to the given cluster to

a degree greater than a specied threshold a P 0Y 1 are used to obtain the estimate:

Zi fzkjmik b aY k 1Y 2Y F F F YNgY i 1Y 2Y F F F Y cX (6)

Recall that our Z contains the owvolumepressure triplets, zk VkY VkYPkT.

Hence, assuming a local linear model (1), any least-squares estimation method can be

applied to estimate the local respiratory elastance E, resistance R and the elastic recoil

pressure P0.

Note, that while all three parameters can easily be estimated in the global model (1), only

some of these parameters can be estimated locally. For instance, in the expiration phase,

there is no ow imposed and the expiration is a free-run process described by a rst-order

differential equation

V t V 0Y (7)

where t is a time constant to be estimated. The following section gives more details on the

analysis of expiration data.

4. Application of fuzzy clustering to respiratory data

Fuzzy clustering can be applied either to the entire respiratory cycle (or several cycles)

or to the inspiration and expiration separately. The former approach is useful for the

detection of those parts of the respiratory cycle that are well described by local linear

models and thus yield more reliable and accurate parameter estimates. This method is

briey outlined in Section 4.1. By clustering the inspiration and expiration data separately,

insight can be gained in the dependence of respiratory parameters on variables like the

volume, for instance. This method has been investigated in more detail and its applicationto the analysis of the expiratory time constant is described in Section 4.2.

4.1. Clustering of the entire respiratory cycle

In this section, the application of fuzzy clustering to the entire respiratory cycle is

demonstrated. It is well known, that the parameters of (1) may vary during the respiratory

cycle [4]. This variability is caused by the fact that the underlying phenomena are actually

nonlinear. Rather than assuming a particular form of the nonlinearity, we propose to use



9/15

fuzzy clustering to automatically nd segments of the cycle that are well explained by local

linear models and thus yield reliable parameter estimates. Fig. 3 shows an example of a

partitioning obtained by clustering the variables VY VYP into four clusters (this numberwas chosen quite arbitrarily).

Note that the obtained segmentation of the cycle is different from a manual splitting into

inspiration and expiration. For instance, the initial samples of inspiration and expiration are

not included. The reason for this is that these data samples are not well explained by the

local linear model estimated for the rest of the phase. This is typically due to nonlinear

phenomena taking place at the transition between the different phases. By adjusting the a-level, the number of samples included in the given local linear model can be controlled.

Large a values will result in more separation between the segments (more data samples will

be discarded). The partitioning can, of course, be obtained from a data sequence consisting

of several cycles (see Fig. 1). This improves the quality of the partitioning, as well as the

subsequent estimation of the respiratory parameters.

4.2. Clustering of expiration data

In this section, only the clustering of expiration data is considered. The goal is to reveal

the dependency of the expiratory time constant on the volume. The expiration data are

obtained by extracting the parts of the cycles between the end of the inspiratory pause andthe beginning of the next cycle. This is done by a simple detection algorithm, clustering is

not used at this stage. The reason for not using fuzzy clustering is that here we are interested

in the nonlinearity. Hence, the complete expiration phase is extracted.

As the expiration is a free-run process described by a rst-order differential equation (7),

only the time constant t can be estimated and analyzed. The columns ofZ are thus the

volumeow pairs: zk VkY VkT

. In each subset obtained by clustering, the time

constant t is estimated. The trend of t among the local models found yields useful

information about the subject's condition.

Fig. 3. Partitioning of the entire respiratory cycle. The phases are obtained by applying the a-cut (6) witha 0X8.



10/15

Fig. 4 shows a typical result obtained by clustering the expiratory data for a patient

without COPD. The expiratory owvolume curve is characterized by a smooth transition

between the initial and later part of the curve. Note the decreasing trend of the time constant

with decreasing volume (bottom plot).

A typical result for a patient with COPD is given in Fig. 5. An abrupt transition is

observed from a small to a large time constant between the initial and the later part of

expiration. The time constant increases with decreasing volume.

Fig. 6 clearly shows the distinction between the patients with and without COPD. In thisgure, the trend of the expiratory time constant t at the beginning of expiration

Dt t2 t1v2 v1

(8)

is plotted versus the average expiration time constant in clusters 2 and 3, t2 t3a2. Here,v1 and v2 denote the volume coordinate of the rst and second cluster center, respectively.

The large difference between the time constant in cluster 1 and the consecutive clusters

in the patients with COPD is also apparent in Table 2. Table 1 shows the pattern for the non-

COPD group.

Fig. 4. Patient without COPD. Top: volumeow-rate data partitioned into four clusters. Middle: the

membership degrees of the four clusters plotted against the volume data. The a 0X8 threshold is shown as well.Bottom: the time constants of the four local models plotted against the volume coordinate vi of cluster centers

(linearly interpolated).



11/15

Fig. 5. Patient with COPD. Top: volumeow-rate data partitioned into four clusters. Middle: the membership

degrees of the four cluster plotted against the volume data. The a 0X8 threshold is shown as well. Bottom: thetime constants of the four local model plotted against the volume coordinate of cluster centers (linearly

interpolated).

Table 1

Time constant for patients without COPD

Data set Cluster 1 Cluster 2 Cluster 3 Cluster 4

cont1 0X60 0X03 0X51 0X02 0X42 0X01 1X60 0X00cont2 0X83 0X01 0X73 0X01 0X59 0X01 0X51 0X04cont3 1X16 0X01 0X97 0X00 0X76 0X01 1X12 0X02cont4 1X11 0X01 0X81 0X01 0X62 0X02 3X22 0X01cont5 1X09 0X01 0X88 0X05 1X03 0X02 1X13 0X01cont6 0X44 0X03 1X29 0X02 1X50 0X02 2X08 0X02cont7 0X56 0X01 0X88 0X01 1X47 0X01 2X49 0X01cont8 0X74 0X01 1X22 0X00 1X18 0X00 1X43 0X01cont9 0X27 0X08 0X79 0X03 1X25 0X02 1X55 0X02cont10 0X63 0X02 0X96 0X01 1X55 0X01 2X23 0X01



12/15

Fig. 6. The trend Dt at the beginning of expiration, dened by Eq. (8), plotted versus the average expiration

time constant in clusters 2 and 3 (t2 t3a2). The two groups of patients are clearly visible (`o' with COPD,`' without COPD).

Table 2

Time constant for patients with COPD

Data set Cluster 1 Cluster 2 Cluster 3 Cluster 4

copd1 0X22 0X19 3X59 0X02 6X75 0X01 8X04 0X01copd2 0X32 0X06 1X39 0X01 3X03 0X01 6X29 0X01copd3 0X32 0X05 1X40 0X01 2X05 0X01 2X47 0X01copd4 0X14 0X15 1X55 0X01 2X21 0X01 3X01 0X01copd5 0X15 0X10 0X84 0X04 3X36 0X01 12X34 0X00copd6 0X51 0X03 2X42 0X01 3X77 0X01 4X93 0X01copd7 0X18 0X06 1X53 0X01 2X49 0X01 3X15 0X01copd8 0X14 0X08 2X11 0X01 2X95 0X01 5X15 0X01copd9 0X51 0X03 1X69 0X01 2X86 0X01 4X15 0X01copd10 0X77 0X05 3X49 0X01 4X98 0X02 5X17 0X02



13/15

5. Discussion and conclusions

This study shows that in mechanically ventilated patients with and without COPD, fuzzyclustering can be applied to assess respiratory parameters. In previous studies we have

shown that the plot of the expiratory ow versus expired volume (expiratory owvolume

curve) provides information about mechanical properties of the respiratory system [20,21].

The inverse of the slope of these curves can be interpreted as a time constant, describing

lung emptying. Mostly, a specic part of the curve (the latter part) is used to calculate a

single time constant. In this study we applied a method based on automatic detection of

multiple local linear models which enables the description of the time constant behavior of

the whole curve.

There is a clear difference in the shape of the expiratory owvolume curve between

patients with and without COPD [20,2224]. In patients without COPD, the expiratory

owvolume curve is mostly characterized by a smooth transition between the initial andlater part of the curve. In patients with COPD, however, an abrupt transition is observed

from a small to a large time constant between the initial and the later part of expiration.

This is caused by airway compression, related to both a decreased lung elastic recoil and an

increased airway resistance in those patients. Fig. 6 clearly shows the distinction between

the groups with and without COPD. The large difference between the time constant in

cluster 1 and the consecutive clusters in the patients with COPD is also apparent in Table 2.

Table 1 shows the pattern for the non-COPD group. Patients 1 to 5 have normal or even stiff

(brotic) lungs. These patients were ventilated because of muscular weakness or pul-

monary brosis due to radiotherapy. Patients 6 to 10 were ventilated for various medical

conditions, but had either mild COPD (FEV1 between 50 and 70% of predicted) or

increased airway resistance. Besides the clear distinction between respiratory mechanics of

patients with and without COPD, fuzzy clustering may discriminate for other pulmonaryconditions, facilitating clinical diagnoses of mechanically ventilated patients in the future.

Besides these applications, the methodology may be useful in other nonlinear estimation

problems in the medicine.



14/15

Appendix A. MATLAB implementation of the GK algorithm



15/15

References

[1] Brunner JX, Laubscher TP, Banner MJ, Iotti G, Braschi A. Simple method to measure total expiratory time

constant based on the passive expiratory owvolume curve. Crit Care Med 1995;23:111722.

[2] Gottfried SB, Rossi A, Higgs BD, et al. Noninvasive determination of respiratory system mechanics during

mechanical ventilation for acute respiratory failure. Am Rev Respir Dis 1985;131:41420.

[3] Gottfried SB, Higgs BD, Rossi A, et al. Interrupter technique for measurement of respiratory mechanics in

anesthetized humans. J Appl Physiol 1985;59:64752.

[4] Peslin R, da Silva F, Duvivier C, Chabot F. Respiratory mechanics studied by multiple linear regression in

unsedated ventilated patients. Eur Respir J 1992;5:8718.

[5] Lauzon AM, Bates JHT. Estimation of time-varying respiratory mechanical parameters by recursive least

squares. J Appl Physiol 1991;71(3):115965.

[6] Avanzolini G, Barbini P. A comparative evaluation of three on-line identication methods for a respiratory

mechanical model. IEEE Trans Biomed Eng 1985;32(11):95763.

[7] Kanazawa K, Kawata Y, Niki N, Satoh H, Ohmatsu H, Kakinuma R, Kaneko M, Moriyama N, Eguchi K.

Computer-aided diagnosis for pulmonary nodules based on helical CT images. Comput Med Imaging

Graphics 1998;22(2):15767.[8] Tolias YA, Panas SM. Fuzzy vessel tracking algorithm for retinal images based on fuzzy clustering. IEEE

Trans Med Imaging 1998;17(2):26373.

[9] Lin JS, Cheng KS, Mao CW. Multispectral magnetic resonance images segmentation using fuzzy Hopeld

neural network. Int J Biomed Comput 1996;42(3):20514.

[10] Zouridakis G, Jansen BH, Boutros NN. Fuzzy clustering approach to EP estimation. IEEE Trans Biomed

Eng 1997;44(8):67380.

[11] Manseld JR, Sowa MG, Scarth GB, Somorjai RL, Mantsch HH. Fuzzy c-means clustering and principal

component analysis of time series from near-infrared imaging of forearm ischemia. Comput Med Imaging

Graphics 1997;21(5):299308.

[12] Lorenz A, Bluem M, Ermert H, Senge Th. Comparison of different neuro-fuzzy classication systems for

the detection of prostate cancer in ultrasonic images. In: Proceedings of the 1997 IEEE Ultrasonics

Symposium, vol. 2, Toronto, Canada, 1997, p. 12014.

[13] Siafakas NM, Vermeire P, Pride NB, et al. Optimal assessment and management of chronic obstructive

pulmonary disease (COPD). The European respiratory task force. Eur Respir J 1995;8:13981420.[14] Gustafson DE, Kessel WC. Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of the IEEE

CDC, San Diego, CA, USA, 1979, p. 7616.

[15] Bezdek JC. Pattern recognition with fuzzy objective function. New York: Plenum Press, 1981.

[16] Gath I, Geva AB. Unsupervised optimal fuzzy clustering. IEEE Trans Pattern Anal Machine Intell

1989;7:77381.

[17] Pal NR, Bezdek JC. On cluster validity for the fuzzy c-means model. IEEE Trans Fuzzy Syst

1995;3(3):3709.

[18] Krishnapuram R, Freg C-P. Fitting an unknown number of lines and planes to image data through

compatible cluster merging. Pattern Recognition 1992;25(4):385400.

[19] Kaymak U, Babuska R. Compatible cluster merging for fuzzy modeling. In: Proceedings FUZZ-IEEE/

IFES'95, Yokohama, Japan, March, 1995, p. 897904.

[20] Lourens MS, van den Berg B, Hoogsteden HC, Bogaard JM. Flowvolume curves as measurement of

respiratory mechanics during ventilatory support: the effect of the exhalation valve. Intensive Care Med

1999;25:799804.

[21] Aerts JG, van den Berg B, Lourens MS, Bogaard JM. Expiratory owvolume curves in mechanically

ventilated patients with chronic obstructive pulmonary disease. Acta Anaesthesiologica Scandinavica

1999;43:3227.

[22] Morris MJ, Lane DJ. Tidal expiratory ow patterns in airow obstruction. Thorax 1981;36:13542.

[23] Aerts JG, van den Berg B, Bogaard JM. Ventilator-CPAP with the Siemens Servo 900C compared with

continuous ow-CPAP in incubated patients: effect on work of breathing. Anaesth Intensive Care

1997;25:48792.

[24] Morris MJ, Madgwick RG, Collyer I, Denby F, Lane DJ. Analysis of expiratory tidal ow patterns as a

diagnostic tool in airow obstruction. Eur Respir J 1998;12:11137.


Article Babuska

Documents

Transcript of Article Babuska